On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

By Sezgin Sucu, Gürhan Içöz, S. Varma. 2012

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This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.

Subfields: Applied Mathematics, Numerical Analysis, Statistics and Probability

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